Fractons, symmetric gauge fields and geometry

TL;DR

This paper explores the connection between gapless fracton phases, higher rank symmetric gauge fields, and geometry, proposing that these gauge theories relate more closely to gravity than traditional gauge theories.

Contribution

It constructs gauge fields for systems conserving charge and dipole moments in curved backgrounds and discusses their relation to spacetime symmetries and gravity.

Findings

Higher rank gauge fields couple to conserved charges and moments.

These gauge theories resemble gravitational fields more than standard gauge theories.

Framework for understanding fracton phases in curved spacetime environments.

Abstract

Gapless fracton phases are characterized by the conservation of certain charges and their higher moments. These charges generically couple to higher rank gauge fields. In this paper we study systems conserving charge and dipole moment, and construct the corresponding gauge fields propagating in arbitrary curved backgrounds. The relation between the symmetries of these class of systems and spacetime transformations is discussed. In fact, we argue that higher rank symmetric gauge theories are closer to gravitational fields than to a standard gauge theory.